The minimum vertical distance between the graphs of y=2+ sinx and y= cosx is

The minimum vertical distance between the graphs of y=2+ sinx and y= cosx is

A
2
B
1
C
$\sqrt{2}$
D
$2 - \sqrt{2}$

Solution:

$min (2 + \sin x - \cos x) = min [2 + \sqrt{2} \sin (x - \frac{π}{4})] = 2 - \sqrt{2}$

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